Maclaurin series for sin_p with p an Integer greater than 2

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43951595" target="_blank" >RIV/49777513:23520/18:43951595 - isvavai.cz</a>
Result on the web
<a href="https://ejde.math.txstate.edu/" target="_blank" >https://ejde.math.txstate.edu/</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Maclaurin series for sin_p with p an Integer greater than 2
Original language description
We find an explicit formula for the coefficients $alpha_n$, $n in mathbb{N}$, of the generalized Maclaurin series for $sin_p$ provided $p > 2$ is an integer. Our method is based on an expression of the $n$-th derivative of $sin_p$ in the form [ sum_{k = 0}^{2^{n - 2} - 1} a_{k,n} sin_p^{p - 1}(x)cos_p^{2 - p}(x),, quad xin left(0, frac{pi_p}{2}right), ] where $cos_p$ stands for the first derivative of $sin_p$. The formula allows us to compute the nonzero coefficients [ alpha_n = frac{lim_{x to 0+} sin_p^{(np + 1)}(x)}{(np + 1)!},. ]
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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